This invention relates to a mechanical pencil sharpener for non-circular (nonconic) pencils and particularly to a sharpener for those rectangular pencils known as "carpenter's pencils." These are customarily sharpened by the workman or user with a pocket knife, because acceptable mechanical sharpeners have not become available. However, the art shows various attempts have been made to this end, as by sharpening each of the four faces or sides separately. Alternately, an oval base configuration such as exemplified by a cosmetic pencil of the kind used by make-up artists can be produced by multiple pairs of cams, as described in the 1978 U.S. Pat. No. to Galli 4,081,010.